The prime minister will travel to Jakarta on Wednesday, where he will meet with Indonesian President Prabowo Subianto.
Mr Prabowo released a video of his conversation with Mr Albanese after his thumping election win, saying he was "so happy" to see him win another term.
The prime minister told the Indonesian president he wanted Jakarta to be his first visit, not Washington or Beijing.
The first state visit to Indonesia continued a legacy set up by the Howard government, which was symbolic in projecting Australia's identity as being close to Asia, Australian Strategic Policy Institute senior analyst Gatra Priyandita said.
"Albanese is interested in maintaining that image of Australia as being independent of the United States and close to the region," he told AAP.
"There is great interest in Indonesia's developing relationship with both Russia and China, with Indonesia establishing some of its first naval exercises with Russia recently, so it will probably be under discussion."
Reports in April that Moscow was seeking permission from Jakarta for Russian Aerospace Forces aircraft to be based in Indonesia alarmed Canberra.
Indonesian authorities reassured their Australian counterparts that would not be the case, but didn't confirm if the request had been made.
The prime minister went back on a pledge to attend Mr Prabowo's inauguration in October 2024, because of a visit to Australia by King Charles.
Dr Gatra said his concern was that the visit would be purely symbolic.
"I haven't heard much in the context of practical deliverables," he said.
"It's very important for Australia and Indonesia to think about strategic co-operation ... especially since both Albanese and Prabowo will likely be counterparts for quite some time."
Concerns about what the increasing presence of the US military in the region means for overall strategic competition might also come up in discussions, Dr Gatra said.
Australia and Indonesia signed a defence co-operation agreement last August.
In a letter to Mr Albanese, Human Rights Watch urged Australia to make the ongoing crisis in Myanmar a focus of its discussions with Mr Prabowo.
It says the two leaders should work together to strengthen multilateral efforts including the use of targeted sanctions to pressure the junta to end violations of human rights.
The human rights organisation also called on Australia to promote equitable responsibility sharing for the resettlement of Rohingya refugees.
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